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Comment by dkokelley | Hacker News Reader

This method helps to improve the expected value from a lotto ticket (though it's still far less than the ticket price), but I'm curious what happens if someone purchases one of every combination. I hear that the odds of winning are something like 1 in 292 million. If it's only $2/ticket, isn't it nearly a sure thing to buy 292 million sequential tickets? Aside from splitting the jackpot with others, your expected outlay is $584 million, and your return is ($1.5 billion)/(number of winners). As long as there are < 3 winners, your expected return is 1.5-3x your investment.

Aside from the feasibility of buying/tracking 292 million tickets and the risk of > 3 winners, am I missing anything?

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Unfortunately, yes. Present value of a future annuity (taking the lump sum now cuts the jackpot by quite a bit), and taxes. For ballpark calculations, I assume that each is going to cut the advertised jackpot in half. So for a $1.5 billion jackpot, your expected return is going to be a around $375 million (plus every single other prize, but that just adds about $20 million to the total), assuming no other winners.

Yes, your strategy will work, but not until the jackpot reaches even more ludicrous heights.

Is the tax something that a hedge fund with offshore shell companies and other active investments could work around?

I seem to recal that Canada doesn't tax winnings.

And there's a better strategy then playing every number; play only the numbers that are not likely to cause a collision. You might not an every time, but you'll increase EV

Canada doesn't tax winnings in games of chance. If you're seen to be operating a business though - a professional poker player for instance - the winnings will be taxed. Buying all the numbers to a lottery with an expected profit could definitely fall under that umbrella.

Under that scenario, you'd be able to deduct the cost of the tickets as a business expense.

True. Would still reduce your net profit though. (And if your plan fails and you don't make a profit, I can just about guarantee they won't allow it to be classified as a business with deductible losses.)

The feasibility of buying 292 million tickets (as you mention) is a key barrier: many lotteries (Powerball included) explicitly and deliberately require that tickets must be bought in person. So, just as a matter of time constraints, you'd need a (nontrivial) army.

Rough ballpark: 300 million combos - let's say you buy 6000 tickets/hour (which I think is actually optimistic probably by a full order of magnitude), for 25 hours a day (assume shifts and magic days), you're still looking at 2,000 person-days.

Or essentially, running a Bitcoin mining pool in real life.

It has been attempted on a lottery where only ~7 million tickets needed to be purchased, but they only managed to buy ~5 million.

http://www.nytimes.com/1992/02/25/us/group-invests-5-million...

$1.5B is only if you take the payments.

It's something like $900 million lump sum.

Good point. A more nuanced calculation would look at the discount rate for that money, but even then it seems like better odds than Vegas.

Minus taxes.

Taxes, for one.

If I remember right (and IANAL) you can deduct gambling losses from gambling winnings (but not ordinary income), so you'd only be paying tax on difference.

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